Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

2 CONSISTENCY WITH EQNS. OF TYPE -d[A]/dt = k[A]"[BIb 381Distribution Sum of squares Degrees of Mean 'freedom squareof group meansfrom set mean("between" groups)c z w(k,,)(-R*--R)'u=u i=r.u=1 1=1(s.s.1)u- 1s.s.1u- 1-of observations fromU=Y i=r, s.s.2group mean ("within" c W(k*')(k,--R*)' r-uu=1 i=1r-ugroups)(s.s.2)-The computations are greatly simplified if the weights w(kJ are equal. For thenthe required sums of squares can be calculated from the quantitiesu=uT =cTov= 1kit, r, and r. Replacing each weighting factorw(kui) by unity, we haveU=Y i=r.u=uS.S.1 = c c T,' TZ(Ev-E)2 = c ---u= 1 i=1 u=i ru ru=u I =ru u=u i=r. u=u ~2s.s.2 = ctogether with the values 1:; c:='Iyu= 1Finally, -. if the set of rate coefficients is homogeneous, the 'best' value is theweighted mean &, viz.The standard error of the weighted mean of the rate coefficients of the whole setcan be estimated from the larger of the two estimates of the variance of the distribution.These two estimates areu=ums, = cu= 1U=UmsZ = CRefmences p. 407u= 1